We analyze repayment incentives in an infinite horizon competitive economy where agents cannot commit to financial contracts. We follow Bulow and Rogoff (1989) by assuming that a defaulting agent is excluded from borrowing forever but keeps the ability to save. Hellwig and Lorenzoni (2009) proved that self-enforcing and not-too-tight debt limits can form a bubble (or discounted martingale) at equilibrium. They also show that when debt limits form a bubble, then the equilibrium outcomes (prices and consumption) are the same as in a model without private debt but with unbacked public debt. The contribution of this paper is to show that bubbles are the only debt limits that are self-enforcing and not too tight. Our characterization is obtained without imposing any ad-hoc boundedness assumption on the endogenous debt limits.